generalized dominance relations that can be computed on one and two mode networks.
positional_dominance(A, type = "one-mode", map = FALSE, benefit = TRUE)Matrix containing attributes or relations, for instance calculated by indirect_relations.
A string which is either 'one-mode' (Default) if A is a regular one-mode network
or 'two-mode' if A is a general data matrix.
Logical scalar, whether rows can be sorted or not (Default). See Details.
Logical scalar, whether the attributes or relations are benefit or cost variables.
Dominance relations as matrix object. An entry [u,v] is 1 if u is dominated by v.
Positional dominance is a generalization of neighborhood-inclusion for
arbitrary network data. In the default case, it checks for all pairs \(u,v\) if
\(A_{ut} \ge A_{vt}\) holds for all \(t\) if benefit = TRUE or
\(A_{ut} \le A_{vt}\) holds for all \(t\) if benefit = FALSE.
This form of dominance is referred to as dominance under total heterogeneity.
If map=TRUE, the rows of \(A\) are sorted decreasingly (benefit = TRUE)
or increasingly (benefit = FALSE) and then the dominance condition is checked. This second
form of dominance is referred to as dominance under total homogeneity, while the
first is called dominance under total heterogeneity.
Brandes, U., 2016. Network positions. Methodological Innovations 9, 2059799116630650.
Schoch, D. and Brandes, U., 2016. Re-conceptualizing centrality in social networks. European Journal of Applied Mathematics 27(6), 971-985.
library(igraph)
data("dbces11")
P <- neighborhood_inclusion(dbces11)
comparable_pairs(P)
#> [1] 0.1636364
# positional dominance under total heterogeneity
dist <- indirect_relations(dbces11, type = "dist_sp")
D <- positional_dominance(dist, map = FALSE, benefit = FALSE)
comparable_pairs(D)
#> [1] 0.1636364
# positional dominance under total homogeneity
D_map <- positional_dominance(dist, map = TRUE, benefit = FALSE)
comparable_pairs(D_map)
#> [1] 0.8727273